I posted this on another forum, but hopefully it makes sense here as well.
Most people seem to confuse ‘logic’ with ‘reason’, like somehow they're the same thing. But in realty, they're not. Logic is to reason as Newtonian Physics is to Relativity. Logic is limited in scope while reason is limitless. Let me explain.
I want you to join in a game with me: its a language game called MUI. The objective is to get from an initial word to a goal word. Here, we will start with the word MI. Your task is to manipulate 'MI', using the rules outlined below, until you get to the goal word MUIU. This might be a little confusing, so I will work through another example first. Read through the rules, and my example proof, and then give it a shot yourself.
RULE I: If you possess a string who’s last letter is ‘I’, you can add on a U at the end.
RULE II: Suppose you have Mx. then you may add Mxx to your collection.
Examples: 'MII' ->'MIIII'
'MUI' -> 'MUIUI'
RULE III: If III occurs in one of the strings in your collection, you may make a new string with U in place of III.
Examples: 'MIIIU' -> 'MUU'
'MIII' -> 'MU'
RULE IV: If UU occurs inside one of your strings, you can drop it.
Examples: 'MUU' -> 'M'
'MUUI' -> 'MI'
As promised, I will work through an example problem first so you get an idea of how the game works. I will transform 'MI' into 'MUI'. Here goes:
By RULE II, you can transform 'MI' into 'MII'. By RULE II again, you can transform 'MII' into 'MIIII'. By RULE III, you can transform 'MIIII' into 'MUI'. Therefore 'MI' - > 'MUI'
Now that you have an idea of how the game works, I want you to try it yourself. Try transforming 'MI' into 'MIU' using the rules outlined above, and put your SENTENCE into the format I provided above. If 'MIU' is unreachable, I want you to spend a minute trying to figure out why. If it IS reachable however, try coming up with your own word that you know cannot be reached using the rules above.
You may not realize it, but the game you've just played has another name. It has another more well respected label called mathematics. For those of you that are not familiar with the more abstract, esoteric branches of mathematics, this might sound a little strange. But I promise, its true. The only difference between this, and the stuff real mathematicians do is that the 'words' mathematicians use have real meaning while the words in this game do not. In fact, if you actually did the exercise, you might have realized something. You might have realized the SENTENCE you wrote isn't just any ordinary sentence. It has a technical term in math called a 'proof'. And the goal word is called a theorem. That's right, if you did the exercise, you successfully proved a mathematical theorem: albeit a completely and utterly useless one.
But why did I get you to play this game? What was the point? Well, I didn't just get you to prove a mathematical theorem. I also made you use logic. That's right, the process of writing out your proof is called 'logic'. Logic, generally speaking, is the application of a set of rules to a set of premises to derive conclusions or theorems. In this game, logic is the application of a set of rules to an initial word to derive a goal word. Are you seeing the symmetry? If you've been following up until this point, hopefully you can see what logic really is. Its a formal process used to derive theorems from premises, or conclusions from axioms. But what you may not have realized yet is why reason and logic are not the same thing.
'MUI' is a game with an alphabet, words and a limited set of rules. It has an alphabet with the letters 'M', 'U' and 'I'. You can construct any word you want, so long as they start with 'M', and you have a set of rules that you can use to manipulate them. If you want to reach a theorem word from some initial word, you must use MUI's laws of logic to get there. This whole game is a 'logical system' with its own alphabet, premises, rules and theorems. But there are more 'logical systems'. In fact, the entirety of mathematics is nothing more than a giant cornucopia of 'logical systems'. It is a conglomeration of richly abstracted 'logical systems' that can be used to prove all sorts of wonderful things about mathematical objects. Mathematics is so brilliantly exciting, but there is a question looming here. One that that will provide you with the key for what distinguishes 'logic' from 'reason'. If mathematics is nothing more than a collection of 'logical systems', then how were those systems discovered?
This seems like an innocuous question, but it has some very serious implications. Think about it for a moment, how were these 'logical systems' discovered? They can't have been discovered using logic, because they ARE the logics themselves. Thus, strictly speaking, unless there is some yet unspecified 'super system' that we use to derive all these other systems, there has to be an explanation. And the explanation, I believe, is called reason. Reason is how mathematicians can devise all of these unique 'logical systems' that are so useful. I know this is quite a jump, but lets take a look at a real world example.
Euclidean geometry is a system we are all familiar with. Euclidean geometry, sometimes called parabolic geometry, is a geometry that follows a set of propositions that are based on Euclid's five premises. If you don't understand what this means, do not fret, I will explain. Here are the 5 definitions or postulates.
Collinear points: points that lie on the same straight line or line segment. Points A, B, and C are collinear.
Line Segment: a straight line with two endpoints. Lines AC, EF, and GH are line segments
Ray: a part of a straight line that contains a specific point. Any of the below line segments could be considered a ray
Intersection point: the point where two straight lines intersect, or cross. The point I is the intersection point for lines EF and GH.
Midpoint: a point in the exact middle of a given straight line segment. Point B is the midpoint of line AC
Euclid came up with a whole book full of definitions that are used to derive all known shapes in 2d space. But more amazingly, he managed to give us a way of understanding the relationship between two sides of a triangle, for example. Or two points on a circle. The important question to ask here, however, is how did he discover these postulates? He could not have derived them from some 'logical system' because geometry constitutes a logical system in its own right. In my opinion, what he did, was work through multiple different sets of postulates, test them by deriving theorems, and them carefully decide which ones made sense, and which ones did not. As Einstein put it, he used reason and creativity to devise his postulates.
This is essentially what distinguishes logic from reason. As Einstein put it, logic can get you from A to B, but imagination will take you everywhere. Logical will get you from one point in a logical system to another. But reason and creativity will get you everywhere. Hopefully this makes sense to you.
